| Since their original work of Prescott, Lucas, and Mehra, among others, the idea of a recursive competitive equilibrium has found extensive applications in many fields of economics, including macroeconomics, industrial organization, asset pricing, and public finance. A recursive competitive equilibrium is a type of sequential equilibrium where equilibrium decision rules are time invariant and there exist support prices consistent with the equilibrium. The existence and characterization of such support prices have been achieved using applications of so-called "Negishi methods", which exploit the second welfare theorem. For Pareto optimal homogeneous agent economies, conditions under which recursive competitive equilibrium exists are well-known. For heterogeneous agent case, results are also available.;Unfortunately, little is known about the validity of such constructions for infinite horizon nonoptimal economies. This is the central question of this dissertation. For nonoptimal economies, standard Negishi methods are known to fail. To address this failure, I develop a new collection of "iterative" Negishi methods. For homogeneous one-sector nonoptimal economies, I construct a Negishi method where the fictitious social planner solves collections of pure resource allocation problems where the dynamic distortions are parameterized by "aggregate" laws of motion. An iterative algorithm is developed that computes candidate support prices consistent with social planning decisions for these aggregate laws of motion. I then use this "equilibrium" social planning problem to construct a duality argument in infinite dimensional spaces to represent price systems that support the aggregate laws of motion and are consistent with a sequential equilibrium.;Next, I extend my iterative Negishi method to heterogeneous agent nonoptimal one-sector economies. First, given aggregate consumption, the planner allocates goods across agents within the period. Then I develop a dynamic programming problem where the planner chooses her equilibrium investment using the value function. Fixed points are then computed. I provide reasonable conditions under which fixed point procedures used to solve equilibrium side conditions in aggregate laws of motion are continuous in the underlying Negishi weights by applying a version of the Bonsall-Nadler theorem, and construct support prices for the sequential equilibrium. |
